Have the DNA polymerase can complete leading-strand synthesis in the ends of DNA, or no, leaving 5'-overhangs? I am interesting in the problem of DNA end replication, and in some literature I have find a data, describing two mechanisms for this problem - first, that polymerase before the catalytic centre also have an anchor centre, and when it comes close to the extremal end of the template, the enzyme will dissociate from the DNA molecule, leaving the last nucleotides uncopied (as the catalytic centre cannot approach to the end); second - removal of the RNA primers. Is the first mechanism really existing???

Eukaryotic chromosomes have telomeres which shorten with each replication, a possibly source of aging as cells with short telomeres are targets of apoptosis (programmed cell death). So yes, it really happens.